Theorems · Definition · algebraic topology
SSet.stdSimplex.faceSingletonIso
{n : ℕ} → (i : Fin (n + 1)) → SSet.stdSimplex.obj { len := 0 } ≅ (SSet.stdSimplex.face {i}).toSSetGiven i : Fin (n + 1), this is the isomorphism from Δ[0] to the face
of Δ[n] corresponding to {i}.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement · cited by 19,642
- Finsetstatement · cited by 13,712
- Oppositestatement · cited by 8,081
- CategoryTheory.Isostatement · cited by 3,963
- SimplexCategorystatement · cited by 2,204
- SSetstatement · cited by 1,283
- SSet.stdSimplexstatement · cited by 499
- SSet.Subcomplex.toSSetstatement · cited by 315
- SSet.stdSimplex.facestatement · cited by 77
- SSet.stdSimplex.faceRepresentableByproof · cited by 1
- SSet.stdSimplex.isoOfRepresentableByproof · cited by 1
- Fin.orderIsoSingletonproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- SSet.stdSimplex.faceSingletonIso_one_hom_comp_ι_eq_δstatement · cited by 1
- SSet.stdSimplex.faceSingletonIso_zero_hom_comp_ι_eq_δstatement · cited by 1
- SSet.horn₂₁.isPushoutproof · cited by 0
- SSet.horn₂₂.isPushoutproof · cited by 0
- SSet.stdSimplex.faceSingletonIso_one_hom_comp_ι_eq_δ_assocstatement and proof · cited by 0
- SSet.stdSimplex.faceSingletonIso_zero_hom_comp_ι_eq_δ_assocstatement and proof · cited by 0
- SSet.horn₂₀.isPushoutproof · cited by 0